Les décisions politiques sur les risques environnementaux complexes font fréquemment intervenir des éléments scientifiques contestés. Il n’y a généralement pas de « faits » qui conduisent à une politique correcte unique. Les éléments de preuve qui sont intégrés dans les avis scientifiques destinés à une décision politique nécessitent une évaluation de leur qualité. En 2003, l’Agence néerlandaise d’évaluation environnementale a adopté une méthode standardisée, désignée sous le nom de « guide », dans le cadre de laquelle les principaux aspects de (...) la production et de l’utilisation des connaissances sont présentés grâce à une liste de contrôle visant à l’évaluation et à la communication des incertitudes. Dans cet article, nous présentons des résultats de l’application de ce guide à la controverse sur les risques des particules en suspension. La délibération active sur l’incertitude dans un contexte d’expertise entraîne un processus d’apprentissage commun entre les experts et les décideurs politiques, ce qui conduit à une meilleure prise de conscience du phénomène d’incertitude et de ses implications politiques.Policy decisions on complex environmental risks often involve disputed science. Typically, there are no “ facts” to support a single unequivocally correct policy. The evidence provided in scientific studies for policy-making decisions requires high-quality assessment. In 2003, the Netherlands Environmental Assessment Agency adopted a standardized method, referred to as “guidelines”, whereby key quality aspects of knowledge production and use are presented in the form of a checklist for uncertainty assessments and communication. In this article, we present the outcomes of applying the guidelines in controversies on the risks of ambient particulate matter. In the policy–advisory context, active deliberation on uncertainty produces a common learning process for advisors and policy makers, which leads to a deeper understanding and increased awareness of the phenomenon of uncertainty and its policy implications. (shrink)

Sarah C. (Sally) Humphreys (S.H.), aujourd’hui professeur émérite d’histoire à l’Université du Michigan (Ann Arbor), a tout au long de sa carrière académique consacré ses recherches aux institutions politiques, sociales et religieuses des cités grecques antiques, plus particulièrement aux époques archaïque et classique ; une partie de ses travaux a d’ores et déjà été réunie dans de précédentes publications (notamment Anthropology and the Greeks, 1978 ; The Family, Women and Death, 1983 ; The...

© 2017. The American Astronomical Society. All rights reserved.We present new observations of the low-mass companion to HD 984 taken with the Gemini Planet Imager as a part of the GPI Exoplanet Survey campaign. Images of HD 984 B were obtained in the J and H bands. Combined with archival epochs from 2012 and 2014, we fit the first orbit to the companion to find an 18 au orbit with a 68% confidence interval between 14 and 28 au, an eccentricity (...) of 0.18 with a 68% confidence interval between 0.05 and 0.47, and an inclination of 119°with a 68% confidence interval between 114°and 125°. To address the considerable spectral covariance in both spectra, we present a method of splitting the spectra into low and high frequencies to analyze the spectral structure at different spatial frequencies with the proper spectral noise correlation. Using the split spectra, we compare them to known spectral types using field brown dwarf and low-mass star spectra and find a best-fit match of a field gravity M6.5 ±1.5 spectral type with a corresponding temperature of K. Photometry of the companion yields a luminosity of log=2.88 ± 0.07 dex with DUSTY models. Mass estimates, again from DUSTY models, find an age-dependent mass of 34 ±1 to 95 ±4 M Jup. These results are consistent with previous measurements of the object. (shrink)

We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.

Provability, Computability and Reflection.

In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure, the ultrapower ofmoduloDis denoted byD-prod. The ultrapower is important because it is a method of constructing structures which are elementarily equivalent to a given structure. Our ultimate aim is to find out what kinds of structure are ultrapowers of. We made a beginning in [5] by proving that, assuming the generalized continuum hypothesis, for (...) each cardinalαthere is an ultrafilterDover a set of powerαsuch that for all structures,D-prodisα+-saturated. (shrink)

Let T be a complete theory with infinite models in a countable language. The stability function g T (κ) is defined as the supremum of the number of types over models of T of power κ. It is proved that there are only six possible stability functions, namely $\kappa, \kappa + 2^\omega, \kappa^\omega, \operatorname{ded} \kappa, (\operatorname{ded} \kappa)^\omega, 2^\kappa$.

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [10]. This logic has quantifiers like $\exists ^{ \ge 3/4} y$ which says that "for at least 3/4 of all y". These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifier $\exists ^{ \ge r} y$ , where y is a tuple (...) of variables. 2. We remove the closedness restriction, which requires that the variables in y occur in all atomic subformulas of the quantifier scope. 3. Instead of the unbiased measure where each model with universe n has the same probability, we work with any measure generated by independent atomic probabilities pR for each predicate symbol R. 4. We extend the results to parametric classes of finite models (for example, the classes of bipartite graphs, undirected graphs, and oriented graphs). 5. We extend the results to a natural (noncritical) fragment of the infinitary logic with probability quantifiers. 6. We allow each pR , as well as each r in the probability quantifier $(\exists ^{ \ge r} y)$ , to depend on the size of the universe. (shrink)

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01].We introduce an operation existsn on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a corollary, if (...) the first order quantifiers are not already absorbed in V, then both the quantifier alternation hierarchy and the existential quantifier hierarchy in the positive first order closure of V are strict.We generalize and simplify methods from Marcinkowski [Mar99] to uncover limitations of the expressive power of an additional first order quantifier, and show that for a wide class of properties S, S cannot belong to the positive first order closure of a monadic prefix class W unless it already belongs to W.We introduce another operation alt on properties which has the same relationship with the Circuit Value Problem as reach has with the Directed Reachability Problem. We use alt to show that Πn⊈ FO, Σn⊈ FO, and Δn+1⊈ FOB, solving some open problems raised in [Mat98]. (shrink)

In a nonstandard universe, the $\kappa$-saturation property states that any family of fewer than $\kappa$ internal sets with the finite intersection property has a nonempty intersection. An ordered field $F$ is said to have the $\lambda$-Bolzano-Weierstrass property iff $F$ has cofinality $\lambda$ and every bounded $\lambda$-sequence in $F$ has a convergent $\lambda$-subsequence. We show that if $\kappa < \lambda$ are uncountable regular cardinals and $\beta^\alpha < \lambda$ whenever $\alpha < \kappa$ and $\beta < \lambda$, then there is a $\kappa$-saturated nonstandard (...) universe in which the hyperreal numbers have the $\lambda$-Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second order arithmetic. (shrink)

Introduction. This paper is a sequel to our paper [3]. In that paper we introduced the notion of a finite approximation to an infinitely long formula, in a language L with infinitely long expressions of the type considered by Henkin in [2]. The results of the paper [3] show relationships between the models of an infinitely long sentence and the models of its finite approximations. In the present paper we shall apply the main result of [3] to prove a number (...) of theorems about ordinary finitely long sentences; these theorems are of a type which one might call “preservation theorems”. The following two known results are typical preservation theorems: A sentence φ is preserved under substructures if and only if φ is equivalent to some universal sentence ; φ is preserved under homomorphic images if and only if φ is equivalent to some positive sentence. An expository account of preservation theorems may be found in Lyndon [9].We shall use freely all of the notation introduced in [3], and shall not attempt to make this paper selfcontained. However, the reader should have no difficulty following this paper after he has read [3]. In § 1 we cover some preliminary topics. In § 2 and § 3 we shall illustrate our method in familiar situations by proving anew the two preservation theorems mentioned above. We shall then obtain four new preservation theorems in §§ 4, 5, and 6, involving respectively direct powers and roots, strong homomorphisms and retracts, and direct factors. The result in § 6 was stated in the abstract [4], while the results in § 5 were stated in the abstract [5]. (shrink)

§0. Introduction. In [16], Barwise described his graduate study at Stanford. He told of his interactions with Kreisel and Scott, and said how he chose Feferman as his advisor. He began working on admissible fragments of infinitary logic after reading and giving seminar talks on two Ph.D. theses which had recently been completed: that of Lopez-Escobar, at Berkeley, on infinitary logic [46], and that of Platek [58], at Stanford, on admissible sets.Barwise's work on infinitary logic and admissible sets is described (...) in his thesis [4], the book [13], and papers [5]—[16]. We do not try to give a systematic review of these papers. Instead, our goal is to give a coherent introduction to infinitary logic and admissible sets. We describe results of Barwise, of course, because he did so much. In addition, we mention some more recent work, to indicate the current importance of Barwise's ideas. Many of the central results are stated without proof, but occasionally we sketch a proof, to indicate how the ideas fit together.Chapters 1 and 2 describe infinitary logic and admissible sets at the time Barwise began his work, circa 1965. From Chapter 3 on, we survey the developments that took place after Barwise appeared on the scene.§1. Background on infinitary logic. In this chapter, we describe the situation in infinitary logic at the time that Barwise began his work. We need some terminology. By a vocabulary, we mean a set L of constant symbols, and relation and operation symbols with finitely many argument places. As usual, by an L-structureM, we mean a universe set M with an interpretation for each symbol of L. (shrink)

Shelah's theory of forking is generalized in a way which deals with measures instead of complete types. This allows us to extend the method of forking from the class of stable theories to the larger class of theories which do not have the independence property. When restricted to the special case of stable theories, this paper reduces to a reformulation of the classical approach. However, it goes beyond the classical approach in the case of unstable theories. Methods from ordinary forking (...) theory and the Loeb measure construction from nonstandard analysis are used. (shrink)

L’auteur étudie les contraintes procédurales qui pèsent sur les procédures d’appel, notamment à la suite des décrets dits “Magendie”. Il montre en regard tous les avantages potentiels apportés par la nouvelle Charte de présentation des écritures et conclut en examinant les déterminants du choix de l’avocat et de son client d’interjeter on de ne pas interjeter d’appel.

A general metatheorem is proved which reduces a wide class of statements about continuous time stochastic processes to statements about discrete time processes. We introduce a strong language for stochastic processes, and a concept of forcing for sequences of discrete time processes. The main theorem states that a sentence in the language is true if and only if it is forced. Although the stochastic process case is emphasized in order to motivate the results, they apply to a wider class of (...) random variables. At the end of the paper we illustrate how the theorem can be used with three applications involving submartingales. (shrink)

In prior work [7] we considered networks of agents who have knowledge bases in first order logic, and report facts to their neighbors that are in their common languages and are provable from their knowledge bases, in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any deciderʼs sentence that can be proved from the combined knowledge base. This paper introduces a (...) more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when it is possible to prepare in advance a finite plan to generate reports within the network. We obtain conditions under which such a plan exists and is guaranteed to produce the right choice under any new observations. (shrink)

Gaifman's normal form theorem showed that every first-order sentence of quantifier rank n is equivalent to a Boolean combination of “scattered local sentences”, where the local neighborhoods have radius at most 7n−1. This bound was improved by Lifsches and Shelah to 3×4n−1. We use Ehrenfeucht–Fraïssé type games with a “shrinking horizon” to get a spectrum of normal form theorems of the Gaifman type, depending on the rate of shrinking. This spectrum includes the result of Lifsches and Shelah, with a more (...) easily understood proof and with the bound on the radius improved to 4n−1. We also obtain bounds for a normal form theorem of Schwentick and Barthelmann. (shrink)

The separation, uniformization, and other properties of the Borel and projective hierarchies over hyperfinite sets are investigated and compared to the corresponding properties in classical descriptive set theory. The techniques used in this investigation also provide some results about countably determined sets and functions, as well as an improvement of an earlier theorem of Kunen and Miller.